Consumer price index are obtained by:

1. Paasche’s formula

2. Fisher’s ideal formula

3. Marshall Edgeworth formula

4. Family budget method formula

Using the standard normal table, the sum of the probabilities to the right of z = 2.18 and to the left of z = -1.75 is:

1. 0.4854

2. 0.4599

3. 0.0146

4. 0.0547

A probability ·density function may be represented by :

1. table

2. graph

3. mathematical equation

4. both (b) and (c)

ഽ\(\sqrt { { e }^{ x } } \) dx is

1. \(\sqrt { { e }^{ x } } +c\)

2. \(2\sqrt { { e }^{ x } } \) + c

3. \(\frac12\sqrt { { e }^{ x } } +c\)

4. \(\frac { 1 }{ 2\sqrt { { e }^{ x } } } +c\)

The particular integral of the differential equation f(D)y = e^ax where f(D) = (D−a)²

1. \(\frac { { x }^{ 2 } }{ 2 } { e }^{ ax }\)

2. xe^ax

3. \(\frac { x }{ 2 } \)e^ax

4. x²e^ax

The LCL for R chart is given by

1. \({ D }_{ 2 }\bar { R } \)

2. \({ D }_{ 2 }\overset { = }{ R } \)

3. \({ D }_{ 3 }\overset { = }{ R } \)

4. \({ D }_{ 3 }\bar { R } \)

In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is

1. 0.0613

2. 0.613

3. 0.00613

4. 0.3913

If X is a discrete random variable and p x ( ) is the probability of X , then the expected value of this random variable is equal to

1. \(\sum { f(x) } \)

2. \(\sum { [x+f(x)] } \)

3. \(\sum { f(x)+x } \)

4. \(\sum { xp(x) } \)

Lagrange’s interpolation formula can be used for

1. equal intervals only

2. unequal intervals only

3. both equal and unequal intervals

4. none of these.

Which of the following is not possible in probability distribution?

1. Σp(x)\(\ge\)0

2. Σp(x)=0

3. Σxp(x)=2

4. p(x)=-0.5

The component of a time series attached to long term variation is trended as

1. Cyclic variation

2. Secular variations

3. Irregular variation

4. Seasonal variations

\(\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } } \) dx is

1. 1

2. 2\(\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } } \)dx

3. 0

4. \({ e }^{ { x }^{ 4 } }\)

If MR and MC denotes the marginal revenue and marginal cost functions, then the profit functions is

1. P = ഽ(MR − MC) dx + k

2. P = ഽ(MR + MC) dx + k

3. P = ഽ(MR)(MC)dx + k

4. P = ഽ(R −C)dx + k

If X is a discrete random variable., then which of the following is correct?

1. 0 \(\le\) F(x) \(\le\) 1

2. F(-\(\infty \)) = 0, F(\(\infty \)) \(\le\) 1

3. P(X = X_n) = F(X_n) - F(X_n-1)

4. F(x) is a constant function

The differential equation of x² + y² = a²

1. xdy + ydx = 0

2. ydx – xdy = 0

3. xdx – ydx = 0

4. xdx + ydy = 0

Which of the following is the homogeneous differential equation?

1. (3x−5)dx = (4y−1)dy

2. xy dx−(x³+y³)dy = 0

3. y²dx+(x² − xy  − y²)dy = 0

4. (x²+y)dx = (y²+x)dy

If \(\rho (A)=\rho (A,B)\)= the number of unknowns, then the system is

1. Consistent and has infinitely many solutions

2. Consistent and has a unique solution

3. inconsistent

4. consistent

The demand function for the marginal function MR = 100 − 9x² is

1. 100 − 3x²

2. 100x − 3x²

3. 100x − 9x²

4. 100 + 9x²

\(\left| { A }_{ n\times n } \right| \)=3 \(\left| adjA \right| \) =243 then the value n is

1. 4

2. 5

3. 6

4. 7

A random sample is a sample selected in such a way that every item in the population has an equal chance of being included

1. Harper

2. Fisher

3. Karl Pearson

4. Dr. Yates

ഽ\(\frac { sin2x }{ 2sinx } dx\) is

1. sin x + c

2. \(\frac12\)sin x + c

3. cos x + c

4. \(\frac12\)cos x + c

The demand and supply function of a commodity are D(x) = 25 − 2x and S(x) = \(\frac { 10+x }{ 4 } \) then the equilibrium price P₀ is

1. 5

2. 2

3. 3

4. 10

The probability function of a random variable is defined as

X=x	-1	-2	0	1	2
P(x)	K	2K	3K	4K	5K

Then k is equal to

1. zero

2. \(\frac{1}{4}\)

3. \(\frac{1}{15}\)

4. one

Given E(X +c ) =8 and E(X- c) = 12, then the value of c is

1. -2

2. 4

3. -4

4. 2

A time series is a set of data recorded

1. Periodically

2. Weekly

3. successive points of time

4. all the above

A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls lasts less than 180 seconds?

1. 0.214

2. 0.094

3. 0933

4. 0.067

Monthly expenditure on their credit cards, by credit card holders from a certain bank, follows a normal distribution with a mean of  Rs.1,295.00 and a standard deviation of Rs.750.00. What proportion of credit card holders spend more than Rs.1,500.00 on their credit cards per month?

1. 0.487

2. 0.392

3. 0.500

4. 0.791

If A= \(\begin{pmatrix} 2 & 0 \\ 0 & 8 \end{pmatrix}\),then \(\rho (A)\) is

1. 0

2. 1

3. 2

4. n

An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is

1. 240/729

2. 489/729

3. 496/729

4. 251/729

If X is a continuous random variable. then P(X\(\ge\)a) = ________.

1. P(X < a)

2. 1-P(X > a)

3. P (X > a)

4. 1-P(X \(\le \) a-1)

If c is a constant in a continuous probability distribution, then p(x = c) is always equal to

1. zero

2. one

3. negative

4. does not exist

In a degenerate solution number of allocations is

1. equal to m+n–1

2. not equal to m+n–1

3. less than m+n–1

4. greather than m+n–1

The distribution function F(x) is equal to

1. P(X = x)

2. P(X \(\le\) x)

3. P(X \(\ge\) x)

4. all of these

A variable that can assume any possible value between two points is called

1. discrete random variable

2. continuous random variable

3. discrete sample space

4. random variable

For the standar-d normal distribution

A	B
1) Area under the curve	(a) 99.74%
2) Area between z = - 1 and z = 1	(b) 95.44%
3) Area between z = - 2 and z = 2	(c) 68.26%
4) Area between z = - 3 and z = 3	(d) 1

The correct match is

1. 1-a, 2-b, 3-c, 4 - d

2. 1 - b, 2 - c, 3 - d, 4 - a

3. 1-d, 2 - c, 3 - b, 4 - a

4. 1-c, 2-d, 3-a, 4 - b

The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, the probability that he hits the target is

1. 1

2. 1 - (0.7)¹⁰

3. (0.7)¹⁰

4. (0.3)¹⁰

The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84?

1. 0.683

2. 0.954

3. 0.271

4. 0.340

E[X-E(X)] is equal to

1. E(X)

2. V(X)

3. 0

4. E(X) - X

The parameters of the normal distribution f(x) = \(\left( \frac { 1 }{ \sqrt { 72\pi } } \right) \frac { { e }^{ -(x-10)^{ 2 } } }{ 72 } \)-\(\infty\)<x<\(\infty\)

 

1. (10,6)

2. (10,36)

3. (6,10)

4. (36,10)

The rank of m×n matrix whose elements are unity is

1. 0

2. 1

3. m

4. n

\(\Gamma (1)\) is

1. 0

2. 1

3. n

4. n!

If probability \(P[|\breve { \theta } -\theta |<\varepsilon ]\rightarrow 1\mu \quad as\quad n\rightarrow \infty ',\) for any positive \(\varepsilon \) then \(\breve { \theta } \) is said to _____________ esitimator of \(\theta\).

1. efficient

2. sufficient

3. unbiased

4. consistent

Using the standard normal table, the sum of the probabilities to the right of z = 2.18 and to the left of z = -1.75 is:

1. 0.4854

2. 0.4599

3. 0.0146

4. 0.0547

∇ ≡

1. 1+E

2. 1 - E

3. 1− E⁻¹

4. 1+ E⁻¹

IfA =\(\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right) \)  then the rank of AA^T is

1. 0

2. 1

3. 2

4. 3

\(\int _{ 0 }^{ \frac { \pi }{ 3 } }{ tanx } dx\) is

1. log 2

2. 0

3. log\(\sqrt { 2 } \)

4. 2 log 2

___________ is a relative property, which states that one estimator is efficient relative to another.

1. efficiency

2. sufficiency

3. unbiased

4. consistency

Which one is not an example of random experiment?

1. A coin is tossed and the outcome is either a head or a tail

2. A six-sided die is rolled

3. Some number of persons will be admitted to hospital emergency room during any hour

4. All medical insurance claims received by a company in a given year

Solution for transportation problem using __________method is nearer to an optimal solution.

1. NWCM

2. LCM

3. VAM

4. Row Minima

The transportation problem is said to be unbalanced if _________

1. Total supply ≠ Total demand

2. Total supply = Total demand

3. m = n

4. m+n–1

The probability that a normal variate X lies in the interval (\(\mu - \sigma, \mu + \sigma\)) is

1. 0.0027

2. 0.9973

3. 0.6826

4. 0.9544

Which of the following Index number satisfy the time reversal test?

1. Laspeyre’s Index number

2. Paasche’s Index number

3. Fisher Index number

4. All of them

\(\int _{ 0 }^{ 4 }{ \left( \sqrt { x } +\frac { 1 }{ \sqrt { x } } \right) } \)dx is

1. \(\frac{20}{3}\)

2. \(\frac{21}{3}\)

3. \(\frac{28}{3}\)

4. \(\frac{1}{3}\)

If p(x)=\(\frac{1}{10}\), c=10, then E(X) is

1. zero

2. \(\frac{6}{8}\)

3. 1

4. -1

ഽ\(\frac { sin5x-sinx }{ cos3x } \)dx

1. −cos2x + c

2. −cos2x + c

3. \(-\frac14\)cos2x c

4. −4cos2x + c

When x₀ = 5 and p₀ = 3 the consumer’s surplus for the demand function p_d = 28 − x² is

1. 250 units

2. \(\frac{250}{3}\)units

3. \(\frac{251}{2}\) units

4. \(\frac{251}{3}\) units

Monthly expenditure on their credit cards, by credit card holders from a certain bank, follows a normal distribution with a mean of Rs.1295.00 and a standard deviation of Rs.750.00. What proportion of credit card holders spend more than Rs.1,500.00 on their credit cards per month?

1. 0.487

2. 0.392

3. 0.500

4. 0.791

In a parametric distribution the mean is equal to variance is :

1. binomial

2. normal

3. poisson

4. all the above

Which one is not an example of random experiment?

1. A coin is tossed and the outcome is either a head or a tail

2. A six-sided die is rolled

3. Some number of persons will be admitted to a hospital emergency room during any hour.

4. All medical insurance claims received by a company in a given year.

Using the factorial representation of the gamma function, which of the following is the solution for the gamma function \(\Gamma \)(n) when n = 8

1. 5040

2. 5400

3. 4500

4. 5540

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

1. 40

2. \(\frac{41}{2}\)

3. \(\frac{40}{3}\)

4. \(\frac{41}{5}\)

ഽ\(\frac { { 2x }^{ 3 } }{ 4+{ x }^{ 4 } } \)dx is

1. \(log\left| 4+{ x }^{ 4 } \right| +c\)

2. \(\frac { 1 }{ 2 } log\left| 4+{ x }^{ 4 } \right| +c\)

3. \(\frac { 1 }{4 } log\left| 4+{ x }^{ 4 } \right| +c\)

4. \(log\left| \frac { { 2x }^{ 3 } }{ { 4+x }^{ 4 } } \right| +c\)

An estimator is said to be __________ if it contains all the information in the data about the parameter it estimates.

1. efficient

2. sufficient

3. unbiased

4. consistent

The complementary function of \(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } -\frac { dy }{ dx } \) = 0 is

1. A + Be^x

2. (A + B)e^x

3. (Ax + B)e^x

4. Ae^x + B

Probability which explains x is equal to or less than particular value is classified as

1. discrete probability

2. cumulative probability

3. marginal probability

4. continuous probability

The solution for an assignment problem is optimal if

1. each row and each column has no assignment

2. each row and each column has atleast one assignment

3. each row and each column has atmost one assignment

4. each row and each column has exactly one assignment

	A		B
1.	S.D of X	a.	\(\sigma { x }^{ 2 }\)
2.	V(x)	b.	\(\overset { \infty }{ \underset { -\infty }{ \int } } \)x.f(x)dx
3.	E(X2) - [E(X)]2	c.	+ \(\sqrt { Var(x) } \)
4.	E(X)	d.	V(X)

1. 1-c, 2-d, 3-a, 4-b

2. 1-d, 2-c, 3-b, 4-a

3. 1-c, 2-a, 3-d, 4-b

4. 1-a, 2-d, 3-b, 4-c

Area bounded by y = \(\left| x \right| \) between the limits 0 and 2 is

1. 1sq.units

2. 3 sq.units

3. 2 sq.units

4. 4 sq.units

The value of \(\int _{ 2 }^{ 3 }{ f(5-x) } dx-\int _{ 2 }^{ 3 }{ f(x) } dx\) is

1. 1

2. 0

3. -1

4. 5

The degree of the differential equation \(\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3\)

1. 1

2. 2

3. 3

4. 4